How can we move meshes for dental occlusion?
I don't believe this can be done with precision having only the open-jaw position. For the future, you may try CT scanning both the open and closed positions - then you can overlay the open jaw mesh onto the rest position.

Also it doesn't help that we only have the left side of the jaw to work with in this scan.

But those issues aside, let's try to work with what we have for the sake of this test.

Techniques that may help:


Use the Mask Modifier to hide all of the mesh except the teeth. Get everything else out of the way. Use Grow Selection to select the verts in hard-to-reach places, then add them to the Vertex Group that is to be masked in.
Set the Origin Point of each object to be on the tooth with the largest surface area, which we know makes contact. That's a good starting point to start making adjustments to location and rotation of the object.
Turn on Backface Culling so that you can see (from behind) when teeth are intersecting.
Familiarize yourself with all of the rotation and location transform operations in Blender, because you will need to use them to get this even close to being correct.
Split your viewport to look at this from at least two different views at once. It will help you assess the position.


How enabling Back-face Culling can help:



Since I advised learning more about rotation, here are some quick rotation/transform tips:


Hitting R twice (RR) will give you a free-orbiting rotation that is often very helpful.
Familiarize yourself with the different Pivot types.
Knowing all of the Snap methods (ShiftS) will help you get your 3D Cursor wherever you want.
Anywhere your 3D Cursor can be, you can set your object's Origin Point to be there using ShiftCtrlAltC) or the button in your Tools Panel.
In addition to the standard Global orientation, at least learn Local and Normal as well if you haven't already. 
ShiftCtrl + Num1, Num3, or Num7 will align your view to the Normal of a selected face.


Here's a .blend with some changes I made. I wouldn't call it accurate, just better than before. I'm not liable for how this is used. Please don't go building anyone's dental implants based on it. ;-)